Johannes Andersen? chair ID  

Compare them to these marked ones.  Google is your friend: 
http://www.lauritz.com/en/auction/johannes-andersen-dining-chairs-model-...

Google is one of my best friends, but there is a lot of misinformation too.  There are some that are marked Danish with screw plugs, a Dixie set with screw plugs, Danish without screw plugs.  Even one of the chairs in the linked set has what appears to be a screw hole from a repair.  Mine do look identical to the stamped pair though.
 
Dixie:  http://www.ebay.com/itm/Set-of-4-Vntg-Mid-Century-Danish-Modern-Johannes...
Uldum Mobilfabrik: http://www.ebay.com/itm/Set-of-4-Vntg-Mid-Century-Danish-Modern-Johannes...
Vamo Mobilfabrik:  https://www.1stdibs.com/furniture/seating/dining-room-chairs/johannes-an...
 
It looks the Dixie chairs have button screw plugs, the Uldum Mobilfabrik chairs have dome screw plugs, and the Vamo Mobilfabrik are without any screw plugs. So I guess Vamo Mobilfabrik is the manufacturer of my chairs?

I understand your frustration; I stared at that Dixie set on eBay for 20min and couldn't spot a significant difference.
I just picked up six of these chairs, and they're marked Uldum.  They do have the "domed" plugs.  If you have any other specific questions, feel free to post here or hit me up via email at michael at themidcenturybeehive dotcom

These are two good comparison pictures I could find of the Dixie chairs vs the marked Uldum chairs.  Apart from the button plugs, the Dixie chair has thicker legs and the connection to the seat back is positioned slightly higher on the leg.
@MidCenturyBeehive would it be possible for you to get a few dimensions?  Seat bottom height, seat back height, width?

Vamo is likely the first manufacturer, because the company was in the habit of naming many of their models. I checked my 57 Vamo catalog these aren't in it. Must have been designed a bit later.

Here's all the measurements I could think to grab this morning:
- Front leg - Bottom to front stretcher 14 3/16"
- Front leg - Bottom to seat bottom 17"
- Front leg - Bottom to side stretcher 14 7/16"
- Front leg spread - Under stretchers 15 3/4"
- Back leg - Bottom to back stretcher 12 3/4"
- Back leg - Bottom to side stretcher 12 13/16"
- Back leg - Bottom to seat bottom 15 1/4"
- Back leg spread - Under stretcher 15 1/2"
- Seat back height 30 1/2"
- Seat back width at top joint 17"
- Back stretcher length 16"